Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
176 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #31826544 | C2 | semidirect |
| 3. #31826216 | C2 | semidirect |
| 4. #31826194 | C2 | semidirect |
| 5. #322×C283 | C2 | semidirect |
| 41. C8×C283 | M16 | semidirect |
| 55. C283 | #1594 | semidirect |
| 61. #322 | D283 | semidirect |
| 97. C8 | #17985375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D2264 | 2 |
| #31826544 | 2 |
| #31826216 | 2 |
| #31826194 | 2 |
| #322×C283 | 2 |
| #1594 | 283 |